Math Problem

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 Joined: Wed Nov 30, 2011 6:24 pm
 Location: Madarbari, Chittagong ,Bangladesh.
Math Problem
Find four prime numbers less than 100 which are factor of 3\[
3^{32}2^{32}\]
3^{32}2^{32}\]
 nafistiham
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Re: Math Problem
\[3^{32}2^{32}\]
\[=(3^{16}+2^{16})(3^{16}2^{16})\]
$now,$
\[=3^{16}2^{16}\]
\[=(3^{8}+2^{8})(3^{8}2^{8})\]
$now,$
\[3^{8}2^{8}\]
\[=(3^4+2^4)(3^42^4)\]
\[=97 \cdot 65\]
\[=97 \cdot 5 \cdot 13\]
the next thing i did isn't quite successful
\[3^8+2^8\]
\[=17 \cdot 401\]
so, the answers are
\[5,97,13,17\]
\[=(3^{16}+2^{16})(3^{16}2^{16})\]
$now,$
\[=3^{16}2^{16}\]
\[=(3^{8}+2^{8})(3^{8}2^{8})\]
$now,$
\[3^{8}2^{8}\]
\[=(3^4+2^4)(3^42^4)\]
\[=97 \cdot 65\]
\[=97 \cdot 5 \cdot 13\]
the next thing i did isn't quite successful
\[3^8+2^8\]
\[=17 \cdot 401\]
so, the answers are
\[5,97,13,17\]
Last edited by nafistiham on Fri Dec 02, 2011 3:47 pm, edited 1 time in total.
\[\sum_{k=0}^{n1}e^{\frac{2 \pi i k}{n}}=0\]
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 Posts: 20
 Joined: Wed Nov 30, 2011 6:24 pm
 Location: Madarbari, Chittagong ,Bangladesh.
 nafistiham
 Posts: 829
 Joined: Mon Oct 17, 2011 3:56 pm
 Location: 24.758613,90.400161
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Re: Math Problem
@ataher.sams
i think you didn't notice how big mistakes i did on that post. i didn't even find out $4$ primes.now it's edited and quite fulfilled.
i think you didn't notice how big mistakes i did on that post. i didn't even find out $4$ primes.now it's edited and quite fulfilled.
\[\sum_{k=0}^{n1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please cooperate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please cooperate.

 Posts: 20
 Joined: Wed Nov 30, 2011 6:24 pm
 Location: Madarbari, Chittagong ,Bangladesh.
 nafistiham
 Posts: 829
 Joined: Mon Oct 17, 2011 3:56 pm
 Location: 24.758613,90.400161
 Contact:
Re: Math Problem
could anyone post a better way to functionize
\[2^8+3^8\]
i just used trial and error division process
\[2^8+3^8\]
i just used trial and error division process
\[\sum_{k=0}^{n1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please cooperate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please cooperate.
Re: Math Problem
Why don't you start a new topic on this??
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."  Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."  Sherlock Holmes
 samiul_samin
 Posts: 1004
 Joined: Sat Dec 09, 2017 1:32 pm
Re: Math Problem
This is BdMO National Junior $2008$ problem no $8$.ataher.sams wrote: ↑Wed Nov 30, 2011 6:39 pmFind four prime numbers less than $100$ which are factors of \[
3^{32}2^{32}\]